A theoretical model has been developed to compute the vertical array directional response for surface generated ambient noise in a shallow water environment. The cross spectrum function is based on a normal mode solution to the wave equation in which the effective depth approximation is used to yield closed form solutions for two distinct mode types. The effective depth modes encompass the shallowest grazing angles where the bottom reacts as a pressure release surface to the incident plane waves. The rigid bottom solution takes over as the grazing angle increases and attenuation becomes significant. The computed vertical array beam output was compared to other models including a fast field wavenumber integration method and a multipath eigenray method with mixed results. The results indicated good agreement for both comparisons with the realization that the effective depth model is sensitive to the approximation discontinuity at the mode transition point.